Safety Verification and Control for Collision Avoidance at Road Intersections

Abstract

This paper presents the design of a supervisory algorithm that monitors safety at road intersections and overrides drivers with a safe input when necessary. The design of the supervisor consists of two parts: safety verification and control design. Safety verification is the problem to determine if vehicles will be able to cross the intersection without colliding with current drivers' inputs. We translate this safety verification problem into a jobshop scheduling problem, which minimizes the maximum lateness and evaluates if the optimal cost is zero. The zero optimal cost corresponds to the case in which all vehicles can cross each conflict area without collisions. Computing the optimal cost requires solving a Mixed Integer Nonlinear Programming (MINLP) problem due to the nonlinear second-order dynamics of the vehicles. We therefore estimate this optimal cost by formulating two related Mixed Integer Linear Programming (MILP) problems that assume simpler vehicle dynamics. We prove that these two MILP problems yield lower and upper bounds of the optimal cost. We also quantify the worst case approximation errors of these MILP problems. We design the supervisor to override the vehicles with a safe control input if the MILP problem that computes the upper bound yields a positive optimal cost. We theoretically demonstrate that the supervisor keeps the intersection safe and is non-blocking. Computer simulations further validate that the algorithms can run in real time for problems of realistic size.

A Bottleneck Degree-Based Migrating Birds Optimization Algorithm for the PCB Production Scheduling

“…Initial solutions show significant effect on the performance of the population and a good initial population possesses the traits of better quality of best solutions and higher diversity among solutions [44]. Moreover, as described above, the flexible job shop with recognized bottlenecks involves task allocation and machine assignment.…”

Optimal Coordination and Control of Connected and Automated Vehicles at Intersections via Mixed Integer Linear Programming

“…In this field of research, the earliest challenge is to formulate the problem to achieve smooth traffic flow (to alleviate congestion) and at the same time guaranteeing the safety of passengers (collisionfree passage through the intersection). Through analyzing the literature, some approaches are identified [5]- [12] and basically, they can be categorized into heuristic [5], [6] and optimization [7]- [12] based approaches. In [5] and [6], a novel reservation-based approach has been proposed where each ve-hicle is required to reserve a space-time block in an intersection via an autonomous intersection manager or also known as a coordinator.…”

“…Another interesting approach to formulate the aforementioned problem is based on scheduling technique. Several research efforts in this direction have been obtained for example considering the optimal time interval that each vehicle needs to spend in an intersection [8], [9], considering the optimal time for each vehicle to arrive at an intersection [10], [11], and jobshop scheduling based formulation [12].…”

Coordination of Multiple Vessels Via Distributed Nonlinear Model Predictive Control

“…Common approaches for intersection control rely on the computation of controlled invariant sets and scheduling [1], [2], [3], [4], but typically require a discretization and allocation of the environment and limit their results to systems with order-preserving dynamics. In contrast, our approach operates directly in continuous space via a constrained optimization and applies to arbitrary dynamics.…”